This romance game puts you in the shoes of Saki Inafune, she’s the niece of Mega Man and Soul Sacrifice creator Keiji Inafune. Saki goes to visit her uncle’s theme park because in this world the 46 year old video game creator is a theme park owner. This should be a fun day, but Count Hogstein blows up the Ferris wheel and holds the staff hostage. Saki decides to save her uncle and play in Hogstein’s games with a group of bachelors like Shidou.

Is there some kind of joke I'm missing here? Honest question. I'm seeing if there's some kind of inside joke I'm not in on, because I don't understand why Keiji Inafune is even mentioned at all in the game.

No, there's no joke. He's just a rather prominent figure in Japan. Also, keep in mind he has done cameos for IF games before, with Neptunia. I also believe he worked with them on a game as well. But really, this is just a cameo and it's only his name being used; it's fun for those who know who he is.